WORK AND ENERGY1

Work

Work as you know it means to do something that takes physical or mental effort

But in physics is has a very different meaningThink about the following:

A heavy chair held at arms length for several minutes A student carries a bucket of water carried along a

horizontal path at a constant velocity

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In both cases no work was done on the chair of the bucket even though both required effort

What conclusions can you draw from the two examples about how work is defined in physics?

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Equation for work

When a constant force is applied to an object:

Work is equal to the magnitude of the applied force times the magnitude of the displacement of the object

W=FdWork is not done unless the object is moved

with the action of a force, parallel to the direction of the force.

Since the heavy chair doesn’t not move vertically no work is done on the chair

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Example

How much work is done when a box is pushed with a force of 8 N over a distance of 4 meters?

32 N•mOr, 32 Joules (32 J)

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Two types of work

1) work done against another force (ex: gravity, shooting a bow, friction)

2) work done to change the speed of an object (ex: speeding up or slowing down in a car)

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Do we always push or pull objects directly horizontal?

Components of the forces will have to be found

If the force applied is at an angle to the horizontal, the component that is parallel to the movement will do work on the object

No work is done on the bucket being carried because all the force being applied to the bucket is perpendicular to the displacement.

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The sign of work is important

Work is a scalar quantity (no direction)It can be positive of negativeIt is positive when the direction of

displacement is in the same direction as the force

It is negative when the direction of the displacement is in the opposite direction of the force (i.e. a car slowing down)

Work done by friction would be negative!

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Net Work

Many forces can be acting on an object making it move

In this case each individual force can be doing work on the object

And together the forces can produce a net work:

Wnet = Fnetd

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ENERGY10

Kinetic Energy

If an object is moving, it is capable of doing work

This is called energy of motion, or Kinetic Energy

If you do work on an object and get it moving, it can then do work on other objects

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Kinetic Energy Equation

Kinetic energy = work required to bring an object up to speed from rest, or to bring to rest from a certain speed….therefore

KE=W=Fd where KE is Kinetic EnergyUsing Newton’s 2nd law, this equation can be

derived into it’s final form-Fd=1/2mv2 or KE =1/2mv2

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Work-Kinetic Energy Theorem

The net work on an object is equal to the change in the kinetic energy of the object.

Wnet=ΔKE=KEf-KEi

Or, Wnet=1/2mvf2-1/2mvi

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Example

On a frozen pond, a person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

Given: m=10.0 kg vi= 2.2 m/s

vf= 0 m/s

µk= 0.10

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Equations: Wnet=Fnetd, Wnet=ΔKE=1/2mvf2-1/2mvi

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Ff=µkFN What forces are acting on the sled as it slows

down?Only friction so: Fnet = Ff=0.10·10.0kg·9.81m/s2

= 9.8 NSince vf = 0, Wnet=-1/2mvi2

=-1/2· 10.0kg·(2.2m/s)2

=-24 J

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So finally, since Wnet = Fnetd-24J=9.8N·dd=2.4 m

TA DA!

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Potential Energy17

Potential Energy

Consider an arrow loaded on a bow.Once the arrow is released it will have kinetic

energyBecause of the arrows position (pulled back

on the bow) it has potential to move, it has potential energy

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Gravitational Potential Energy

The energy associated with an object due to the object’s position relative to the gravitational source is called gravitational potential energy

Given by this equationPEg=mgh

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Elastic Potential Energy

Most common objects that have elastic potential energy are springs

When springs are compressed or stretched they have elastic potential energy stored When the force holding the spring in position is removed

the spring will return to its equilibrium position

Length of spring with no external forces is called relaxed length

The amount of energy depends on distance compressed or stretched from its relaxed length

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Elastic Potential can be found using the following equation

PEelastic=1/2kx2

Where – k is the spring constant, of force constant

Spring constants have units of N/m

Example22

When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. The spring constant of the spring is 400.0 N/m. What is the total potential energy of this system?

Given: m=2.00 kg k=400.0 N/m g=9.81 m/s2

h= 50.0 cm = 0.500 m x= 10.0 cm = 0.100 m

Solution23

PEtot= PEg+PEelastic

PEg=mgh

PEelastic=1/2kx2

PEg=2.00kg·9.81 m/s2·0.500m= 9.81 JPEelastic=1/2·400.0 N/m·(0.100 m)2

= 2.00 J9.81 J + 2.00 J = 11.81 J

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Conservation of Energy

Energy is Conserved25

Something is conserved when it remains constant

Like matter, energy cannot be created or destroyed

Energy gets transferred or transformed in to other types of energy

Mechanical Energy26Many objects have both

mechanical and potential energy

For example a swinging pendulum

At the highest point of its swing it has all gravitational potential energy

At the bottom of the pendulum it has all kinetic energy.

Everywhere in between it has both

PEg + KE=Total Energy

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As the pendulum falls from its highest point it gains speed, therefore it is gaining KE

As it falls it is also decreasing its height, therefore PEg is decreasing

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Mechanical energy is the sum of the potential energy and the kinetic energy associated with an object

ME = KE + ΣPE (Σ = sum)

Conservation of Mechanical Energy:In the absence of friction, the total mechanical

energy remains the sameMEi=Mef

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POWER

Power30

Rate at which work is doneRate of energy transferEquation:P=W/tOr, P=Fv (this one is less commonly used, but

just in case…)The unit for power is the Watt